ArticleTitle:CloudfeedbackmechanismsandtheirrepresentationinglobalclimatemodelsArticleType:AdvancedReview

Authors:PauloCeppiDepartmentofMeteorology,UniversityofReading,Reading,UnitedKingdomp.ceppi@reading.ac.ukFlorentBrientCentreNationaldeRecherchesMétéorologiques,Météo-France/CNRS,Toulouse,FranceMarkD.ZelinkaCloudProcessesResearchGroup,LawrenceLivermoreNationalLaboratory,Livermore,UnitedStatesDennisL.HartmannDepartmentofAtmosphericSciences,UniversityofWashington,Seattle,UnitedStates

Abstract

Cloudfeedback–thechangeintop-of-atmosphereradiativefluxresultingfromthecloudresponsetowarming – constitutes by far the largest source of uncertainty in the climate response to CO2forcing simulated by global climate models (GCMs). We review the main mechanisms for cloudfeedbacks, and discuss their representation in climate models and the sources of inter-modelspread. Global-mean cloud feedback in GCMs results from three main effects: (1) rising free-troposphericclouds(apositivelongwaveeffect);(2)decreasingtropicallowcloudamount(apositiveshortwaveeffect);(3)increasinghigh-latitudelowcloudopticaldepth(anegativeshortwaveeffect).These cloud responses simulated by GCMs are qualitatively supported by theory, high-resolutionmodeling, and observations. Rising high clouds are consistent with the Fixed Anvil Temperature(FAT)hypothesis,wherebyenhancedupper-troposphericradiativecoolingcausesanvilcloudtopstoremain at a nearly fixed temperature as the atmosphere warms. Tropical low cloud amountdecreasesaredrivenbyadelicatebalancebetweentheeffectsofverticalturbulentfluxes,radiativecooling, large-scale subsidence, and lower-tropospheric stability on the boundary-layer moisturebudget.High-latitudelowcloudopticaldepthincreasesaredominatedbyphasechangesinmixed-phase clouds. The causes of inter-model spread in cloud feedback are discussed, focusingparticularly on the role of unresolved parameterized processes such as cloud microphysics,turbulence,andconvection.

Graphical/VisualAbstractandCaption

Spatialdistributionof cloud feedback (inWm-2perK surfacewarming)predictedbya setofglobal climatemodelssubjectedtoanabruptincreaseinCO2.RedrawnwithpermissionfromZelinkaetal.(2016).

1

INTRODUCTION2

Astheatmospherewarmsundergreenhousegasforcing,globalclimatemodels(GCMs)predictthat3clouds will change, resulting in a radiative feedback by clouds1, 2. While this cloud feedback is4positiveinmostGCMsandhenceactstoamplifyglobalwarming,GCMsdivergesubstantiallyonits5magnitude3. Accurately simulating clouds and their radiative effects has been a long-standing6challengeforclimatemodeling,largelybecausecloudsdependonsmall-scalephysicalprocessesthat7cannotbeexplicitlyrepresentedbycoarseGCMgrids.IntherecentClimateModelIntercomparison8Project phase 5 (CMIP5)4, cloud feedback was by far the largest source of inter-model spread in9equilibrium climate sensitivity, the global-mean surface temperature response to CO2 doubling5-7.10The important role of clouds in determining climate sensitivity in GCMs has been known for11decades8-11, and despite improvements in the representation of cloud processes12, much work12remainstobedonetonarrowtherangeofGCMprojections.13

Despite these persistent difficulties, recent advances in our understanding of the fundamental14mechanisms of cloud feedback have opened exciting new opportunities to improve the15representation of the relevant processes in GCMs. Thanks to increasing computing power,16turbulence-resolving model simulations have offered novel insight into the processes controlling17marinelowcloudcover13-16,ofkeyimportancetoEarth’sradiativebudget17.Clevercombineduseof18model hierarchies and observations has provided new understanding of why high-latitude clouds19brighten18-20,whytropicalanvilcloudsshrinkwithwarming21,andhowcloudsandradiationrespond20tostormtrackshifts22-24,tonameafewexamples.21

Thegoalof this review is tosummarizethecurrentunderstandingofcloudfeedbackmechanisms,22andtoevaluatetheirrepresentationincontemporaryGCMs.Althoughtheobservationalsupportfor23GCMcloudresponsesisassessed,wedonotprovideathoroughreviewofobservationalestimates24ofcloudfeedback,nordowediscusspossible“emergentconstraints”25.Thediscussionisorganized25into twomainsections.First,wediagnosecloud feedback inGCMs, identifying thecloudproperty26changes responsible for the radiative response. Second,we interpret theseGCMcloud responses,27discussingthephysicalmechanismsatplayandtheabilityofGCMstorepresent them,andbriefly28reviewing the available observational evidence. Based on this discussion, we conclude with29suggestionsforprogresstowardanimprovedrepresentationofcloudfeedbackinclimatemodels.30

DIAGNOSINGCLOUDFEEDBACKINGLOBALCLIMATEMODELS31

Webeginbydocumentingthemagnitudeandspatialstructureofcloudfeedback incontemporary32GCMs,andidentifythecloudpropertychangesinvolvedintheradiativeresponse.Althoughclouds33mayrespondtoanyforcingagent,inthisreviewwewillfocusoncloudfeedbacktoCO2forcing,of34highestrelevancetofutureanthropogenicclimatechange.35

Global-meancloudfeedback36

Theglobal-meancloudfeedbackstrength(quantifiedbythefeedbackparameter;Box1)isplottedin37Fig. 1, along with the other feedback processes included in the traditional decomposition. The38feedbackparametersarederived fromCMIP5experiments forcedwithabruptquadruplingofCO239concentrations relative to pre-industrial conditions. In the following discussion we quote the40

numbersfromananalysisof28GCMs5(coloredcirclesinFig.1).Twootherstudies(greysymbolsin41Fig.1)showsimilarresults,buttheyincludesmallersubsetsoftheavailablemodels.42

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Fig. 1. Strengths of individual global-mean feedbacks and equilibrium climate sensitivity (ECS) for CMIP544models,derivedfromcoupledexperimentswithabruptquadruplingofCO2concentration.Modelnamesand45feedback values are listed in the Supporting Information, Table S1. Feedback parameter results are from46Caldwelletal.5,withadditionalcloudfeedbackvaluesfromVialetal.6andZelinkaetal.26ECSvaluesaretaken47fromAndrewsetal.27,Forsteretal.28,andFlatoetal.29FeedbackparametersarecalculatedasinSodenetal.3048butaccountingforrapidadjustments;thecloudfeedbackfromZelinkaetal.iscalculatedusingcloud-radiative49kernels31 (Box2).Circlesarecoloredaccordingto thetotal feedbackparameter.ThePlanck feedback (mean50valueof-3.15Wm-2K-1)isexcludedfromthetotalfeedbackparametershownhere.51

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Box1:Climatefeedbacks53

IncreasinggreenhousegasconcentrationscauseapositiveradiativeforcingF(Wm-2),towhichthe54climatesystemrespondsbyincreasingitstemperaturetorestoreradiativebalanceaccordingto55

N=F+λ∆T.56

N denotes the net energy flux imbalance at the top of atmosphere, and ∆T is the global-mean57surfacewarming.Howeffectivelywarmingreestablishesradiativebalanceisquantifiedbythetotal58feedback parameter λ (inWm-2 K-1). For a positive (downward) forcing, warmingmust induce a59negative(upward)radiativeresponsetorestorebalance,andhenceλ<0.Whenthesystemreaches60anewsteadystate,N=0andthusthefinalamountofwarmingisdeterminedbybothforcingand61feedback,∆T=–F/λ.Amorepositivefeedbackimpliesmorewarming.62

The total feedback λ equals the sum of contributions from different feedback processes, each of63whichisassumedtoperturbthetop-of-atmosphereradiativebalancebyagivenamountperdegree64warming. The largest such process involves the increase in emitted longwave radiation following65Planck’slaw(anegativefeedback).Additionalfeedbacksresultfromincreasedlongwaveemissionto66spaceduetoenhancedwarmingaloft(negativelapseratefeedback);increasedgreenhousewarming67bywatervapor(positivewatervaporfeedback);anddecreasingreflectionofsolarradiationassnow68andiceretreat(positivesurfacealbedofeedback).Changesinthephysicalpropertiesofcloudsaffect69

boththeirgreenhousewarmingandtheirreflectionofsolarradiation,givingrisetoacloudfeedback70(Box2),positiveinmostcurrentGCMs.71

Themulti-model-meannetcloudfeedback ispositive (0.43Wm-2K-1),suggestingthatonaverage,72clouds cause additionalwarming. However,models produce awide range of values, fromweakly73negativetostronglypositive(-0.13to1.24Wm-2K-1).Despitethisconsiderableinter-modelspread,74only two models, GISS-E2-H and GISS-E2-R, produce a (weakly) negative global-mean cloud75feedback. In the multi-model mean, this positive cloud feedback is entirely attributable to the76longwave(LW)effectofclouds(0.42Wm-2K-1),whilethemeanshortwave(SW)cloudfeedbackis77essentiallyzero(0.02Wm-2K-1).78

Of all the climate feedback processes, cloud feedback exhibits the largest amount of inter-model79spread,originatingprimarilyfromtheSWeffect3,6,26,32.Theimportantcontributionofcloudstothe80spreadintotalfeedbackparameterandequilibriumclimatesensitivity(ECS)standsoutinFig.1.The81net cloud feedback is strongly correlated with the total feedback parameter (r=0.80) and ECS82(r=0.73).83

Box2:Cloud-radiativeeffectandcloudfeedback84

The radiative impact of clouds is measured as the cloud-radiative effect (CRE), the difference85betweenclear-skyandall-skyradiativefluxatthetopofatmosphere.Cloudsreflectsolarradiation86(negative SW CRE, global-mean effect of -45 W m-2) and reduce outgoing terrestrial radiation87(positiveLWCRE,27Wm-2),withanoverallcoolingeffectestimatedat -18Wm-2 (numbers from88Hendersonetal.33).CRE isproportional tocloud fraction,but isalsodeterminedbycloudaltitude89and optical depth. Themagnitude of SW CRE increases with cloud optical depth, and to amuch90lesserextentwithcloudaltitude.Bycontrast,theLWCREdependsprimarilyoncloudaltitude,which91determines the difference in emission temperature between clear and cloudy skies, but also92increaseswithopticaldepth.93

Asthecloudpropertieschangewithwarming,sodoestheirradiativeeffect.Theresultingradiative94flux response at the top of atmosphere, normalized by the global-mean surface temperature95increase, isknownascloudfeedback.This isnotstrictlyequaltothechange inCREwithwarming,96because theCRE also responds to changes in clear-sky radiation – for example due to changes in97surfacealbedoorwatervapor34.TheCREresponsethusunderestimatescloudfeedbackbyabout0.398Wm-2 on average34, 35. Cloud feedback is therefore the component of CRE change that is due to99changingcloudpropertiesonly.100

VariousmethodsexisttodiagnosecloudfeedbackfromstandardGCMoutput.Thevaluespresented101inthispaperareeitherbasedonCREchangescorrectedfornon-cloudeffects30,orestimateddirectly102fromchanges incloudproperties, for thoseGCMsprovidingappropriatecloudoutput31.Themost103accurateprocedureinvolvesrunningtheGCMradiationcodeoffline–replacinginstantaneouscloud104fieldsfromacontrolclimatologywiththosefromaperturbedclimatology,whilekeepingotherfields105unchanged – to obtain the radiative perturbation due to changes in clouds36, 37. This method is106computationallyexpensiveandtechnicallychallenging,however.107

RapidAdjustments108

Thecloud-radiativechangesthataccompanyCO2-inducedglobalwarmingpartlyresultfromarapid109adjustment of clouds to CO2 forcing and land-surfacewarming38, 39. Because it is unrelated to the110global-meansurfacetemperatureincrease,thisrapidadjustmentistreatedasaforcingratherthana111feedbackinthecurrentfeedbackanalysisframework40.Animportantimplicationisthatcloudscause112uncertainty in both forcing and feedback. For a quadrupling of CO2 concentration, the estimated113global-meanradiativeadjustmentduetocloudsrangesbetween0.3and1.1Wm-2,dependingon114theanalysismethodandGCMset,andhasbeenascribedmainlytoSWeffects6,41,42.Accountingfor115thisadjustmentreducesthenetandSWcomponentofthecloudfeedback.Wereferthereaderto116Andrewsetal.43andKamaeetal.44 forathoroughdiscussionofrapidcloudadjustments inGCMs.117Hereafterwefocussolelyonchanges incloudpropertiesthataremediatedby increases inglobal-118meantemperature.119

Decompositionbycloudtype120

For models providing output that simulates measurements taken by satellites, the total cloud121feedback can be decomposed into contributions from three relevant cloud properties: cloud122altitude, amount, and optical depth (plus a small residual)45. The multi-model-mean net cloud123feedback can then be understood as the sum of positive contributions from cloud altitude and124amountchanges,andanegativecontributionfromopticaldepthchanges(Fig.2a).Thevariouscloud125properties have distinctly different effects on LW and SW radiation. Increasing cloud altitude126explainsmostof thepositiveLWfeedback,withminimaleffectonSW.Bycontrast, cloudamount127and optical depth changes have opposing effects on SW and LW radiation, with the SW term128dominating. (Note that 11 of the 18 feedback values in Fig. 2 include the positive effect of rapid129adjustments,yieldingamorepositivemulti-modelmeanSWfeedbackcomparedwithFig.1.)130

ThecloudpropertydecompositioninFig.2acanberefinedbyseparatelyconsideringlow(cloudtop131pressure > 680 hPa) and free-tropospheric clouds (cloud top pressure ≤ 680 hPa), as this more132effectivelyisolatesthefactorscontributingtothenetcloudfeedback26.Thisverticaldecomposition133reveals that themulti-modelmean LW feedback is entirely due to rising free-tropospheric clouds134(Fig.2b).Forsuchclouds,amountandopticaldepthchangesdonotcontributetothenetfeedback135becausetheirSWandLWeffectscancelnearlyperfectly.Meanwhile,theSWcloudfeedbackcanbe136ascribed to low cloud amount and optical depth changes (Fig. 2c). Thus, the results in Fig. 2b,c137highlight the three main contributions to the net cloud feedback in current GCMs: rising free-138troposphericclouds(apositiveLWeffect),decreasinglowcloudamount(apositiveSWeffect),and139increasing lowcloudopticaldepth(aweaknegativeSWeffect),yieldinganetpositivefeedback in140the multi-model mean. It is noteworthy that all CMIP5 models agree on the sign of these141contributions.142

Spatialdistributionofcloudfeedback143

The contributions to LW and SW cloud feedback are far from being spatially homogeneous,144reflecting the distribution of cloud regimes (Fig. 3). Although the net cloud feedback is generally145positive,negative valuesoccurover theSouthernOceanpolewardof about50° S, and toa lesser146extentovertheArcticandsmallpartsofthetropicaloceans.Themostpositivevaluesarefoundin147regions of large-scale subsidence, such as regions of low SST in the equatorial Pacific and the148

subtropicaloceans.Weak tomoderatesubsidenceregimescovermostof the tropicaloceans,and149areassociatedwithshallowmarinecloudssuchasstratocumulusandtradecumulus.InmostGCMs150such clouds decrease in amount17, 46, strongly contributing to the positive low cloud amount151feedback seen in Fig. 2c. This explains the importance of shallow marine clouds for the overall152positive cloud feedback, and their dominant contribution to inter-model spread in net cloud153feedback17.154

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Fig.2.GlobalmeanLW(red),SW(blue),andnet(black)cloudfeedbacksdecomposedintoamount,altitude,156opticaldepth (OD)and residual components for (a)all clouds, (b) free-troposphericcloudsonly,and (c) low157cloudsonly,definedbycloudtoppressure(CTP).Multi-modelmeanfeedbacksareshownashorizontallines.158Resultsarebasedonananalysisof11CMIP3and7CMIP5models26;theCMIP3valuesdonotaccountforrapid159adjustments.Model names and total feedback values are listed in Table S2. Redrawnwithpermission from160Zelinkaetal.26161162

Takinga zonal-meanperspectivehighlights themeridionaldependenceof cloudproperty changes163andtheircontributionstocloudfeedback(Fig.4).Free-troposphericcloudtopsrobustlyriseglobally,164producing a positive cloud altitude LW feedback at all latitudes that peaks in regions of high165climatological free-tropospheric cloud cover (blue curve). The positive cloud amount feedback166(orangecurve),dominatedbytheSWeffectof lowclouds(cf.Fig.2),alsooccursovermostofthe167globe with the exception of the high southern latitudes; by contrast, the effect of optical depth168changes is near zero everywhere except at high southern latitudes, where it is strongly negative169(greencurve).Thisyieldsacomplexmeridionalpatternofnetcloudfeedback(blackcurveinFig.4).170

Thepatternsofcloudamountandopticaldepthchangessuggest theexistenceofdistinctphysical171processesindifferentlatituderangesandclimateregimes,asdiscussedinthenextsection.172

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Fig.3.Spatialdistributionofthemulti-modelmeannetcloudfeedback(inWm-2perKsurfacewarming)ina174set of 11 CMIP3 and 7 CMIP5 models subjected to an abrupt increase in CO2 (Table S2). Redrawn with175permissionfromZelinkaetal.26176

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TheresultsinFig.4allowustofurtherrefinetheconclusionsdrawnfromFig.2.Inthemulti-model178mean,thecloudfeedbackincurrentGCMsmainlyresultsfrom179

• globallyrisingfree-troposphericclouds,180

• decreasinglowcloudamountatlowtomiddlelatitudes,and181

• increasinglowcloudopticaldepthatmiddletohighlatitudes.182

Summary183

Cloud feedback is themain contributor to inter-model spread in climate sensitivity, ranging from184nearzerotostronglypositive(-0.13to1.24Wm-2K-1)incurrentclimatemodels.Itisacombination185of three effects present in nearly all GCMs: rising free-tropospheric clouds (a LW heating effect);186decreasing low cloud amount in tropics tomidlatitudes (a SWheating effect); and increasing low187cloudopticaldepthathighlatitudes(aSWcoolingeffect).Lowcloudamountintropicalsubsidence188regionsdominatestheinter-modelspreadincloudfeedback.189

190

INTERPRETINGCLOUDPROPERTYCHANGESINGLOBALCLIMATEMODELS191

Havingdiagnosedtheradiatively-relevantcloudresponsesinGCM,weassessourunderstandingof192thephysicalmechanismsinvolvedinthesecloudchanges,anddiscusstheirrepresentationinGCMs.193Weconsider in turneachof the threemaineffects identified in theprevioussection,andaddress194thefollowingquestions:195

• What physicalmechanisms are involved in the cloud response? Towhat extent are these196mechanismssupportedbytheory,high-resolutionmodeling,andobservations?197

• How well do GCMs represent these mechanisms, and what parameterizations does this198dependon?199

• Whatexplainstheinter-modelspreadincloudresponses?200

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Fig.4.Zonal-,annual-,andmulti-model-meannetcloudfeedbacksinasetof11CMIP3and7CMIP5models202(TableS2),plottedagainst thesineof latitude,andpartitioned intocomponentsdueto thechange incloud203amount,altitude,andopticaldepth.Curvesaresolidwhere75%ormoreofthemodelsagreeonthesignof204thefeedback,dashedotherwise.RedrawnwithpermissionfromZelinkaetal.26205206

Cloudaltitude207

Physicalmechanisms208

Owingtothedecreaseoftemperaturewithaltitudeinthetroposphere,highercloudtopsarecolder209andthusemitlessthermalinfraredradiationtospace.Therefore,anincreaseinthealtitudeofcloud210topsimpartsaheatingtotheclimatesystembyreducingoutgoingLWradiation.Fundamentally,the211riseofupper-level cloud tops is firmlygrounded inbasic theory (thedeepeningof thewell-mixed212troposphereastheplanetwarms),andissupportedbycloud-resolvingmodelingexperimentsandby213observationsofbothinterannualcloudvariabilityandmulti-decadalcloudtrends.Thecombination214of theoretical and observational evidence, alongwith the fact that all GCMs simulate rising free-215troposphericcloudtopsastheplanetwarms,makethepositivecloudaltitudefeedbackoneofthe216mostfundamentalcloudfeedbacks.217

The tropical free troposphere is approximately in radiative-convective equilibrium, where latent218heating in convective updrafts balances radiative cooling, which is itself primarily due to thermal219emission by water vapor47. Because radiative cooling by the water vapor rotation and vibration220bandsfallsoffrapidlywithdecreasingwatervapormixingratiointhetropicaluppertroposphere48,221sotoomustconvectivemass flux.Hence,massdetrainment fromtropicaldeepconvectionand its222attendantanvilcloudcoveragebothpeaknearthealtitudewhereemissionfromwatervapordrops223offrapidlywithpressure,whichwerefertoasthealtitudeofpeakradiatively-drivenconvergence.224Becauseradiativecoolingbywatervaporiscloselytiedtowatervaporconcentrationandthelatter225

isfundamentallycontrolledbytemperaturethroughtheClausius-Clapeyronequation,thedramatic226decrease in water vapor concentration in the upper troposphere occurs primarily due to the227decreaseof temperaturewithdecreasingpressure.This implies that the level thatmarksthepeak228coverageof anvil cloud tops is setby temperature.As isotherms risewith globalwarming, so too229must tropical anvil cloud tops, leading to a positive cloud altitude feedback. This “fixed anvil230temperature” (FAT) hypothesis49, illustrated schematically in Fig. 5, provides a physical basis for231earlier suggestions that fixed cloud top temperature is amore realistic response towarming than232fixedcloudaltitude50,51.233

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Fig. 5. Schematic of the relationship between clear-sky radiative cooling, subsidence warming, radiatively-235drivenconvergence,andaltitudeofanvilcloudsinthetropicsinacontrolandwarmclimate,asarticulatedin236the FAT hypothesis. Upon warming, radiative cooling by water vapor increases in the upper troposphere,237which must be balanced by enhanced subsidence in clear-sky regions. This implies that the level of peak238radiatively-drivenconvergenceandtheattendantanvilcloudcoveragemustshiftupward.TCdenotestheanvil239cloudtoptemperatureisotherm.240

241

Inpractice, tropicalhighcloudsriseslightly less thanthe isotherms inresponsetomodeledglobal242warming,leadingtoaslightwarmingoftheiremissiontemperature–albeitamuchweakerwarming243thanoccurs at a fixedpressure level (roughly six times smaller)52. This is related toan increase in244upper tropospheric static stability with warming that was not originally anticipated in the FAT245hypothesis.Theproportionatelyhigheranviltemperature(PHAT)hypothesis52allowsforincreasesin246staticstabilitythatcausethelevelofpeakradiatively-drivenconvergencetoshifttoslightlywarmer247temperatures. The upward shift of this level closely tracks the upward shift of anvil clouds under248globalwarming, and captures their slightwarming. The aforementionedupper-tropospheric static249stability increase has been described as a fundamental consequence of the first law of250thermodynamics,whichresultsinstaticstabilityhavinganinverse-pressuredependence21,although251theradiativeeffectofozonehasalsobeenshowntoplayarole53.252

Cloud-resolving(horizontalgridspacing≤15km)modelsimulationsoftropicalradiative-convective253equilibrium support the theoretical expectation that the distribution of free-tropospheric clouds254shifts upwardwith surfacewarming nearly in lockstepwith the isotherms,making their emission255temperatureincreaseonlyslightly53-56.Thisresponseisalsoseeninglobalcloud-resolvingmodels57-25659.This is important forconfirmingthattheresponseseen inGCMs21, 52andmesoscalemodels49 is257not an artifact of parameterized convection. Furthermore, observed interannual relationships258between cloud top altitude and surface temperature are also in close agreementwith theoretical259expectations60-65.Recentanalysesof satellitecloud retrievals showed thatboth tropicalandextra-260tropicalhighcloudshaveshiftedupwardovertheperiod1983-200966,67.261

AlthoughFATwasproposedasamechanismfortropicalcloudaltitudefeedback, it ispossiblethat262radiative cooling by water vapor also controls the vertical extent of extratropical motions, and263thereby the strength of extratropical cloud altitude feedback (Thompson et al., submitted264manuscript). Inanycase, theextratropical free troposphericcloudaltitude feedback inGCMs isat265leastas largeas itscounterpart inthetropics26,despitehavingreceivedmuchlessattentioninthe266literature.267

Box3:FATandthecloudaltitudefeedback268

Cloud tops rising as the surfacewarmsproduces apositive feedback: by rising so as to remain at269nearly constant temperature, their emission to space does not increase in concert with emission270fromtheclear-skyregions,inhibitingtheradiativecoolingoftheplanetunderglobalwarming.271

Thefactthatcloudtoptemperatureremainsroughlyfixedmakestheinterpretationofthefeedback272potentiallyconfusing:howcanhighcloudswarmtheplanet if theiremissiontemperatureremains273nearly unchanged? It is important to recall that feedbacks due to variable X are defined as the274changeinradiationduetothetemperature-mediatedchangeinXholdingallelsefixed68.Inthecase275where X is cloud top altitude, the feedback quantifies the change in radiation due solely to the276change in cloud top altitude, holding the temperature structure of the atmosphere fixed at its277unperturbedstate.Thus, increasedcloudtopaltitudecausesaLWheatingeffectbecause– in the278radiationcalculation–theemissiontemperatureofthecloudtopactuallydecreasesbytheproduct279ofthemean-statelapserateandthechangeinthecloudtopaltitude.280

Animportantpointtoavoidlosinginthedetails isthataslongasthefreetroposphericcloudtops281rise under global warming, the altitude feedback is positive. The extent to which cloud top282temperatureschangeaffectsonlythemagnitudeofthefeedback,notitssign.283

284

Representationinglobalclimatemodelsandcausesofinter-modelspread285

Given its solid foundation in well-established physics (radiative-convective equilibrium, Clausius-286Clapeyronrelation), it isunsurprisingthatallGCMssimulateanearly isothermalrise inthetopsof287free tropospheric cloudswithwarming, inexcellentagreementwithPHAT.Themulti-modelmean288net free-tropospheric cloud altitude feedback is 0.20 W m-2 K-1, with an inter-model standard289deviationof0.09Wm-2K-1(Fig.1b).Althoughthespreadinthisfeedbackisroughlyhalfaslargeas290that in the lowcloudamount feedback, it is still substantialandremainspoorlyunderstood.Since291

thealtitudefeedbackisdefinedastheradiativeimpactofrisingcloudtopswhileholdingeverything292elsefixed(Box3),themagnitudeofthisfeedbackatanygivenlocationshouldberelatedto(1)the293change in free-tropospheric cloud top altitude, (2) the decrease in emitted LW radiation per unit294increaseofcloud topaltitude,and (3) the free-troposphericcloud fraction.Thesearediscussed in295turnbelow.296

Based on the discussion above, one would expect the magnitude of the upward shift of free-297troposphericcloudtops(term1)toberelatedtotheupwardshiftofthelevelofradiatively-driven298convergence.Bothof thesearedependenton themagnitudeofupper troposphericwarming69, 70,299whichvariesappreciablyacrossmodels71,72forreasonsthatremainunclear.300

ThedecreaseinemittedLWradiationperunitincreaseincloudtopaltitudedependsonthemean-301statetemperatureandhumidityprofileoftheatmosphere,andoncloudLWopacity.Totheextent302that inter-model differences in atmospheric thermodynamic structure are small, inter-model303variance in term 2would arise primarily fromdifferences in themean state cloud opacity,which304determineswhetheranupwardshiftisaccompaniedbyalargedecreaseinLWflux(forthickclouds)305or a small decrease in LW flux (for thin clouds). Overall, the dependence of LW fluxes on cloud306optical thickness is small, however, because clouds of intermediate to high optical depth are307completelyopaquetoinfraredradiation.Therefore,wedonotexpectcloudopticaldepthbiasesto308dominatethespreadincloudaltitudefeedback.309

Finally,themean-statefree-troposphericcloudfraction(term3)islikelytoexhibitsubstantialinter-310model spread. A four-fold difference in the simulated high (cloud top pressure ≤ 440 hPa) cloud311fractionwas foundamonganearlier generationofmodels73, though this spreadhasdecreased in312CMIP5models12.Furthermore,climatemodels systematicallyunderestimate the relative frequency313ofoccurrenceoftropicalanvilandextratropicalcirrusregimes74,75.Takenalone,suchbiaseswould314leadtomodelssystematicallyunderestimatingthecloudaltitudefeedback.315

Lowcloudamount316

Physicalmechanisms317

The low cloud amount feedback in GCMs is dominated by the response of tropical, warm, liquid318cloudslocatedbelowabout3kmtosurfacewarming.Severaltypesofcloudsfulfillthedefinitionof319“low”,differingintheirradiativeeffectsandinthephysicalmechanismsunderlyingtheirformation,320maintenance and response to climate change. So far, most insights into low cloud feedback321mechanisms have been gained from high-resolution models – particularly large-eddy simulations322(LES)thatcanexplicitlyrepresenttheturbulentandconvectiveprocessescriticalforboundary-layer323clouds on scales smaller than one kilometer76. The low cloud amount feedback in GCMs is324determined by the response of the most prevalent boundary-layer cloud types at low latitudes:325stratus,stratocumulus,andcumulusclouds.326

Although they cover a relatively small fraction of Earth, stratus and stratocumulus (StCu) have a327largeSWCRE,sothatevensmallchangesintheircoveragemayhavesignificantregionalandglobal328impacts. StCu cloud coverage is strongly controlled by atmospheric stability and surface fluxes77:329observations suggest a strong relationshipbetween inversion strengthat the topof theplanetary330boundarylayer(PBL)andcloudamount78,79.Astrongerinversionresultsinweakermixingwiththe331

dry free troposphere, shallowing the PBL and increasing cloudiness. Since inversion strength will332increase with global warming owing to the stabilization of the free-tropospheric temperature333profile80,onemightexpectlowcloudamounttoincrease,implyinganegativefeedback81.334

However, LES experiments suggest that StCu clouds are sensitive to other factors than inversion335strength, as summarized by Bretherton15. Over subsiding regions, (1) increasing atmospheric336emissivity owing to water vapor feedback will cause more downward LW radiation, decreasing337cloud-top entrainment and thinning the cloud layer (less cloud and hence a positive radiative338feedback); (2) the slowdownof the general circulationwillweaken subsidence, raising cloud tops339and thickening the cloud layer (a negative dynamical feedback); (3) a larger vertical gradient of340specific humiditywill dry thePBLmoreefficiently, reducing cloudiness (apositive thermodynamic341feedback). Evidence for these physical mechanisms is usually also found in GCMs82-84 or when342analyzingobservednaturalvariability85-87.Thereal-worldStCufeedbackwillmost likelyresultfrom343therelativeimportanceoftheseantagonisticprocesses.LESmodelsforcedwithanidealizedclimate344changesuggestareductionofStCucloudswithwarming76.345

Shallow cumuli (ShCu) usually denote clouds with tops around 2-3 km localized over weak346subsidenceregionsandhighersurfacetemperature.DespitetheirmoremodestSWCRE,ShCuareof347major importance to global-mean cloud feedback in GCMs because of theirwidespread presence348acrossthetropics17.YetmechanismsofShCufeedbackinLESarelessrobustthanforStCu.Usually,349LES reduce clouds with warming, with large sensitivity to precipitation (mostly related to350microphysical assumptions). This reduction has been explained by a stronger penetrative351entrainment that deepens and dries the PBL more efficiently13, 88 (closely related to the352thermodynamic feedback seen for StCu), although the strength of this positive feedback may353depend on the choice of prescribed or interactive sea surface temperatures (SSTs)89, 90 and354microphysicsparameterization14.OtherfeedbacksseenforStCumayactonShCubutwithdifferent355relative importance14.AlthoughLESresultssuggestapositiveShCufeedback14,aglobalmodelthat356explicitly resolves the crudest form of convection shows the opposite response91. Hence further357workwithahierarchyofmodelconfigurations(LES,globalcloud-resolvingmodel,GCMs)combined358withobservationalanalyseswillbeneededtovalidatetheShCufeedback.359

Recent observational studies of the low cloud response to changes in meteorological conditions360broadlysupporttheStCuandShCufeedbackmechanismsidentifiedinLESexperiments84,87,92.These361studiesshowthatlowcloudsinbothmodelsandobservationsaremostlysensitivetochangesinSST362and inversion strength.Although these twoeffectswould tend tocanceleachother,observations363andGCMsimulations constrainedbyobservations suggest that SST-mediated low cloud reduction364withwarmingdominates,increasingthelikelihoodofapositivelowcloudfeedbackandhighclimate365sensitivity87, 93-95. Nevertheless, recent ground-based observations of co-variations of ShCu with366meteorological conditions suggest thatamajorityofGCMsareunlikely to represent the temporal367dynamics of the cloudy boundary-layer96, 97. This may reduce our confidence in GCM-based368constraintsofShCufeedbackwithwarming.369

Representationinglobalclimatemodelsandsourcesofinter-modelspread370

Cloud dynamics dependheavily on small-scale processes such as local turbulent eddies, non-local371convective plumes, microphysics, and radiation. Since the typical horizontal grid size of GCMs is372around 50 km, such processes are not explicitly simulated and need to be parameterized as a373

function of the large-scale environment. GCMs usually represent cloud-related processes through374distinct parameterizations, with separate assumptions for subgrid variability, despite a goal for375unification98,99.PhysicalassumptionsusedinPBLparameterizationsoftenrelatecloudformationto376buoyancy production, stability, and wind shear. Low cloud amount feedbacks are constrained by377how these cloud processes are represented in GCMs and how they respond to climate change378perturbations. Sinceparameterizationsareusually crude, it isnotevident that themechanismsof379lowcloudamountfeedbackinGCMsarerealistic.380

AllCMIP5modelssimulateapositivelowcloudamountfeedback,butwithconsiderablespread(Fig3812c);thisfeedbackisbyfarthelargestcontributortointer-modelvarianceinnetcloudfeedback5,17,38226.Spreadinlowcloudamountfeedbackcanbetracedbacktodifferencesinparameterizationsused383inatmosphericGCMs92, 100-102,andchanges in theseparameterizationswithin individualGCMsalso384have clear impacts on the intensity (and sign) of the response102-104. Identifying the low cloud385amountfeedbackmechanismsinGCMsisadifficulttask,however,becausethelowcloudresponse386is sensitive to the competing effects of a variety of unresolved processes. Considering that these387processes are parameterized in diverse and complex ways, it appears unlikely that a single388mechanismcanaccountforthespreadoflowcloudamountfeedbackseeninGCMs.389

Ithasbeenproposedthatconvectiveprocessesplayakeyroleindrivinginter-modelspreadinlow390cloudamount feedback105-110.As theclimatewarms, convectivemoisture fluxes strengthendue to391therobustincreaseoftheverticalgradientofspecifichumiditycontrolledbytheClausius-Clapeyron392relationship82.IncreasingconvectivemoisturefluxesbetweenthePBLandthefreetropospherelead393to a relatively drier PBL with decreased cloud amount, suggesting a positive feedback, but the394degreetowhichconvectivemoisturemixingincreasesseemstostronglydependonmodel-specific395parameterizations109. GCMs with stronger present-day convective mixing (and therefore more396positive low cloud amount feedback) have been argued to compare better with observations109,397implying that convective overturning strength could provide an observational constraint on GCM398behavior. However, running GCMs with convection schemes switched off does not narrow the399spreadofcloud feedback111, suggesting thatnon-convectiveprocessesmayplayan important role400too92,104.401

We believe that inter-model spread in low cloud amount feedback does not depend on the402representationofconvection(deepandshallow)alone,butratherontheinterplaybetweenvarious403parameterized processes – particularly convection and turbulence. It has been argued that the404relative importance of parameterized convective drying and turbulent moistening of the PBL405accounts for a large fraction of the inter-model differences in both the mean state, and global406warmingresponseoflowclouds46.InGCMsthatattributealargeweighttoconvectivedryinginthe407present-day climate, the strengthening ofmoisture transportwithwarming causes enhanced PBL408ventilation,efficiently reducing lowcloudamount109.Conversely if convectivedrying is lessactive,409turbulencemoisteninginduceslowcloudshallowingratherthanachangeincloudamount46,110. In410somemodels,additionalparameterization-dependentmechanismsmaycontributetothelowcloud411feedback,suchascloudamountincreasesbyenhancementofsurfaceturbulence83,112orbychanges412incloudlifetime113.413

Lowcloudopticaldepth414

Physicalmechanisms415

Theprimarycontroloncloudopticaldepthisthevertically-integratedliquidwatercontent,termed416liquidwaterpath (LWP). If othermicrophysical parameters areheld constant, cloudoptical depth417scaleswithLWPwithin thecloud114.Cloudopticaldepth isalsoaffectedbycloudparticlesizeand418cloudicecontent,buttheiceeffectissmallersinceicecrystalsaretypicallyseveraltimeslargerthan419liquiddroplets, and therefore lessefficient at scattering sunlightperunitmass115. Consistentwith420this, the cloud optical depth change maps well onto the LWP response in global warming421experiments,bothquantitiesincreasingatmiddletohighlatitudesinnearlyallGCMs18,19,45,116,117.422Understanding the negative cloud optical depth feedback therefore requires explaining why LWP423increaseswithwarming,andwhyitdoessomostlyathighlatitudes.424

Two plausible mechanisms may contribute to LWP increases with warming, and both predict a425preferentialincreaseathigherlatitudesandlowertemperatures.Thefirstmechanismisbasedupon426the assumption that the liquid water content within a cloud is determined by the amount of427condensationinsaturatedrisingparcelsthatfollowamoistadiabatGm,fromthecloudbasetothe428cloud top118-120. This is often referred to as the "adiabatic" cloud water content. Under this429assumption, it may be shown that the change in LWP with temperature is a function of the430temperature derivative of themoist adiabat slope,¶Gm/¶T. This predicts that the adiabatic cloud431water content always increases with temperature, and increases more strongly at lower432temperaturesinarelativesense118.433

A second mechanism involves phase changes in mixed-phase clouds. Liquid water is commonly434found in clouds at temperatures substantially below freezing, down to about -38°C where435homogeneousfreezingoccurs115,121.Cloudsbetween-38°Cand0°Ccontainingbothliquidwaterand436ice are termed mixed-phase. As the atmosphere warms, the occurrence of liquid water should437increase relative to ice; for a fixed total cloudwater path, thiswould lead to an optically thicker438cloudowingtothesmallereffectiveradiusofdroplets19,115,121.Inaddition,ahigherfractionofliquid439waterisexpectedtodecreasetheoverallprecipitationefficiency,yieldinganincreaseintotalcloud440waterandafurtheropticalthickeningofthecloud19,115,119,121.Reducedprecipitationefficiencymay441also increasecloudlifetime,andhencecloudamount121, 122.Becausethephasechangemechanism442can only operate below freezing, its occurrence in low clouds is restricted to middle and high443latitudes.444

Satelliteandin-situobservationsofhigh-latitudecloudssupportincreasesincloudLWPandoptical445depthwithtemperature18,19,120,andsuggestanegativecloudopticaldepthfeedback20,althoughthis446resultissensitivetotheanalysismethod123.ThepositiveLWPsensitivitytotemperatureisgenerally447restricted tomixed-phase regions and is typically larger than that expected frommoist adiabatic448increasesinwatercontentalone18,19.Thislendsobservationalsupportfortheimportanceofphase449change processes.While themoist adiabaticmechanism should still contribute to LWP increases450withwarming,LESmodelingofwarmboundary-layerclouds(inwhichphasechangeprocessesplay451norole)suggeststhatopticaldepthchangesaresmallrelativetotheeffectsofdryinganddeepening452oftheboundarylayerwithwarming13.453

Representationinglobalclimatemodels454

ThelowcloudopticaldepthfeedbackpredictedbyGCMscanonlybetrustedtotheextentthatthe455drivingmechanismsareunderstoodandcorrectly represented.Wethereforeask,howreliablyare456thesephysicalmechanismsrepresentedinGCMs?Thefirstmechanisminvolvesthesourceofcloud457water from condensation in saturated updrafts. It results from basic, well-understood458thermodynamics that do not directly rely on physical parameterizations, and should be correctly459implemented in allmodels. As such, it constitutes a simple and powerful constraint on the cloud460watercontentresponsetowarming,tothepointthatsomeearlystudiesproposedtheglobalcloud461feedback might be negative as a result124-126. Considering this mechanism in isolation ignores462importantcompetingfactorsthataffectthecloudwaterbudget,however,suchastheentrainment463of dry air into the convective updrafts, phase change processes, or precipitation efficiency. The464competitionbetween these various factorsmayexplainwhyno simple, robust LWP increasewith465temperatureisseeninallregionsacrosstheworldinGCMs.466

The secondmechanism isprimarily related to the liquidwater sink through conversion to iceand467precipitation by ice-phase microphysical processes. The representation of cloud microphysics in468state-of-the-art GCMs is mainly prognostic, meaning that rates of change between the different469phases–vapor,liquid,ice,andprecipitation–arecomputed.Ratherthanbeingadirectfunctionof470temperature(asinadiagnosticscheme),therelativeamountsofliquidandicethusdependonthe471efficienciesof the sourceand sink terms. InGCMs, cloudwaterproduction inmixed-phase clouds472occursmainly in liquid form; subsequent glaciationmay occur through a variety ofmicrophysical473processes,particularlytheWegener-Bergeron-Findeisen127mechanism(seeStorelvmoetal.128fora474descriptionandareview).Ice-phasemicrophysicsarethereforemainlyasinkofcloudliquidwater.475Uponwarming, this sink should become suppressed, resulting in a larger reservoir of cloud liquid476water19.477

InGCMs,theopticaldepthfeedback is likelydominatedbymicrophysicalphasechangeprocesses.478Severallinesofevidencesupportthisidea.Asinobservations,lowcloudopticaldepthincreaseswith479warming almost exclusively at high latitudes, and the increase in cloudwater content is typically480restrictedtotemperaturesbelowfreezing117,129,130–afindingthatcannotbesatisfactorilyexplained481bytheadiabaticwatercontentmechanism. Imposingatemperature increaseonly inthe ice-phase482microphysics explains roughly 80% of the total LWP response to warming in two contemporary483GCMsruninaquaplanetconfiguration19.Furthermore,changesintheefficiencyofphaseconversion484processes have dramatic impacts on the cloud water climatology and sensitivity to warming in485GCMs131-133.486

Causesofinter-modelspread487

AlthoughGCMsagreeon the signof the cloudoptical depth response inmixed-phase clouds, the488magnitude of the change remains highly uncertain. This is in large part because the efficiency of489phasechangeprocessesvarieswidelybetweenmodels,impactingthemeanstateandthesensitivity490towarming116.491

GCMs separately simulate microphysical processes for cloud water resulting from large-scale492(resolved) vertical motions, and convective (unresolved, parameterized) motions. In convection493schemes, microphysical phase conversions are crudely represented, usually as simple, model-494

dependentanalyticfunctionsoftemperature.Whiletherepresentationofmicrophysicalprocessesis495much more refined in large-scale microphysics schemes, ice-phase processes remain diversely496represented due to limitations in our understanding, particularly with regard to ice formation497processes134, 135. In models explicitly representing aerosol-cloud interactions, an additional498uncertainty results from poorly constrained ice nuclei concentrations122. For mixed-phase clouds,499perturbingtheparameterizationsofphasetransitionscansignificantlyaffecttheratioofliquidwater500to ice, the overall cloud water budget, and cloud-radiative properties19, 133. Owing to these501uncertainties, the simple constraint that the liquid water fractionmust increase with warming is502strongbutmerelyqualitativeinGCMs.503

It is believed that mixed-phase clouds may become glaciated too readily in most GCMs121, 128.504Satelliteretrievalssuggestmodelsunderestimatethesupercooledliquidfractionincoldclouds132,136-505138; this may be because models assume too much spatial overlap between ice and supercooled506clouds, overestimating the liquid-to-ice conversion efficiency128. An expected consequence is that507liquidwaterandcloudopticaldepthincreasetoodramaticallywithwarminginGCMs,sincethereis508toomuch climatological cloud ice in a fractional sense. Comparisonswith observations appear to509support that idea18, 20. Suchmicrophysical biases could have powerful implications for the optical510depthfeedback,asmodelswithexcessivecloudicemayoverestimatethephasechangeeffect130,133,511139, 140. Insummary, thecurrentunderstanding is that thenegativecloudopticaldepth feedback is512likelytoostronginmostGCMs.FurtherworkwithobservationaldataisneededtoconstrainGCMs513andconfirmtheexistenceofanegativeopticaldepthfeedbackintherealworld.514

Otherpossiblecloudfeedbackmechanisms:tropicalandextratropicaldynamics515

While themechanismsdiscussed abovearemainly linked to the climate system’s thermodynamic516response to CO2 forcing, dynamical changes could have equally important implications for clouds517and radiation. This poses a particular challenge: not only are the cloud responses to a given518dynamical forcing uncertain141, but the future dynamical response is also much more poorly519constrained than the thermodynamic one142. Belowwediscuss two possible effects of changes in520atmosphericcirculation,oneinvolvingthedegreeofaggregationoftropicalconvection,andanother521basedonextratropicalcirculationshiftswithwarming.Weassesstherelevanceof theseproposed522feedbackprocessesinGCMsandintherealworld.523

Convectiveaggregationandthe“iriseffect”524

Tropical convective clouds both reduce outgoing LW radiation and reflect solar radiation. These525effectstendtooffseteachother,andoverthebroadexpanseofwarmwatersinthewesternPacific526and IndianOcean areas these two effects very nearly cancel, so that net cloud radiative effect is527about zero143-145. The net neutrality of tropical cloud radiative effects results from a cancellation528betweenpositiveeffectsof thinanvil cloudsandnegativeeffectsof the thicker rainyareasof the529cloud146.Thatconvectivecloudstendtoriseinawarmedclimatehasbeendiscussedabove,butitis530alsopossiblethattheopticaldepthorareacoverageofconvectivecloudscouldchangeinawarmed531climate. For high clouds with no net effect on the radiation balance, a change in area coverage532without change in the average radiative properties of the clouds would have little effect on the533energybalance (unless thehigh cloudsaremaskingbright lowclouds).Because the individual LW534andSWeffectsoftropicalconvectivecloudsarelarge,asmallchangeinthebalanceoftheseeffects535couldalsoprovidealargefeedback.536

Sofarmoreattentionhasbeendirectedatoceanicboundary layerclouds,whosenetCRE is large,537sincetheirsubstantialSWeffectisnotbalancedbytheirrelativelysmallLWeffect.ButsincetheSW538effect of tropical convective clouds is as large as that of boundary-layer clouds in stratocumulus539regimes,asubstantialfeedbackcouldoccur iftherelativeareacoverageofthinanvilsversusrainy540cores with higher albedos changes in a way to disrupt the net radiative neutrality of convective541clouds.Relativelylittlehasbeendoneonthisproblem,sinceglobalclimatemodelsdonotresolveor542explicitly parameterize the physics of convective complexes and their associated meso- and543microscaleprocesses.544

Ithasbeenproposed that tropicalanvil cloudareashoulddecrease inawarmedclimate,possibly545causing a negative LW feedback, but the theoretical and observational basis for this hypothesis546remainscontroversial147-151.TheresponseoftropicalhighcloudamounttowarminginGCMsisvery547sensitive to the particular parameterizations of convection and cloud microphysics that are548employed107,152,asmightbeexpected.549

One basic physical argument for changing the area of tropical high cloudswithwarming involves550simple energy balance and the dependence of saturation vapor pressure on temperature35. The551basicenergybalanceoftheatmosphereisradiativecoolingbalancedbylatentheating.Convection552mustbringenough latentheatupwardtobalanceradiative losses.Radiative losses increaserather553slowly with surface temperature (~1.5% per K), whereas the latent energy in the atmosphere554increasesby~7%perKwarming35,153.Ifoneassumesthatlatentheatingisproportionaltosaturation555vaporpressuretimesconvectivemassflux,itfollowsthatconvectivemassfluxmustdecreaseasthe556planet warms35. If the cloud area decreases with themass flux, then the high cloud area should557decreasewithwarming.Somesupportforthismechanismisfoundinglobalcloud-resolvingmodel558experiments57.559

Anothermechanismisthetendencyoftropicaldeepconvectiontoaggregateinpartofthedomain,560leavinganotherpartofthedomainwithlittlehighcloudandlowrelativehumidity.Thisisobserved561to happen in radiative-convective equilibrium models in which the mesoscale dynamics of562convectivecloudsisresolved154-156,althoughtherelevanceofthismechanismtorealisticmodelsand563therealworldremainsunclear.Thepresenceofconvectionmoistensthefreetroposphere,andthe564radiative and microphysical effects of this encourage convection to form where it has already565influencedtheenvironment.Awayfromtheconvection,theairisdryandradiativecoolingsupports566subsidencethatsuppressesconvection.Ithasbeenarguedthatsinceself-aggregationoccursathigh567temperatures,globalwarmingmay leadtoagreaterconcentrationofconvectionthatmayreduce568theconvectiveareaandleadtoacloudfeedback21.Sincetropicalconvectionisalsoorganizedbythe569large-scale circulations of the tropics, and the physics of tropical anvil clouds are not well-570representedinglobalmodels,theseideasremainatopicofactiveresearch.Basicthermodynamics571make the static stability a function of pressure, whichmay affect the fractional coverage of high572cloudsinthetropics21,52.573

Shiftsinmidlatitudecirculationwithglobalwarming574

Atmospheric circulation is a key control on cloud structure and radiative properties157. Because575current GCMs predict systematic shifts of subtropical and extratropical circulation toward higher576latitudes as the planet warms158, it has been suggested that midlatitude clouds will shift toward577regionsofreducedinsolation,causinganoverallpositiveSWfeedback3,159.578

Althoughthispolewardshiftofstorm-trackcloudscountsamongtherobustpositivecloudfeedback579mechanismsidentifiedinthefifthIPCCassessmentreport(Fig.7.11inBoucheretal.3),thepictureis580much lessclear inanalysesofcloud-radiativeresponsestostormtrackshifts inGCMexperiments.581While someGCMs produce a clear cloud-radiative SWdipole in response to storm track shifts160,582others simulate no clear zonal- or global-mean SW response24, 161-163. In the context of observed583variability, theGCMswithno significant cloud-radiative response toa storm-track shift are clearly584moreconsistentwithobservations22, 24.The lackofanobservedSWcloudfeedbacktostormtrack585shiftsresultsfromfree-troposphericandboundary-layercloudsrespondingtostormtrackvariability586in opposite ways. As the storms shift poleward, enhanced subsidence in themidlatitudes causes587free-tropospheric drying and cloud amount decreases, resulting in the expected shift of free-588tropospheric cloudiness. Meanwhile, however, lower-tropospheric stability increases, favoring589enhancedboundary-layercloudinessandmaintainingtheSWCREnearlyunchanged24.Theabilityof590GCMs to reproduce this behavior has been linked to their shallow convection schemes163 and to591their representation of the effect of stability on boundary-layer cloud24. If unforced variability592provides a good analog for the cloud response to forced dynamical changes – thought to be593approximately true in GCMs163 – then the above results suggest little SW radiative impact from594futurejetandstormtrackshifts.595

SinceLWradiationismuchmoresensitivetotheresponseoffree-troposphericcloudsthantolow596cloud changes, storm-track shifts do cause coherent LW cloud-radiative anomalies23. These597anomalies are small in the context of global warming-driven cloud feedback, however23, so that598futureshiftsinmidlatitudecirculationappearunlikelytobeamajorcontributiontoglobal-meanLW599cloud feedback.Given the strong seasonality of LW and SW cloud-radiative anomalies, it remains600possiblethatextratropicalcirculationshiftshavenon-negligibleradiative impactsonseasonaltime601scales164, 165. It isalsopossiblethatcloudsandradiationrespondmorestronglytootheraspectsof602atmospheric circulation than themidlatitude jets and storm tracks; it hasbeen recentlyproposed603thatmidlatitudecloudchangesaremorestronglytiedtoHadleycellshiftsthantothejet165.Further604observationalandmodelingworkisneededtoconfirmtheserelationshipsandassesstheirrelevance605tocloudfeedback.606

607

CONCLUDINGREMARKS608

PossiblepathwaystoanimprovedrepresentationofcloudfeedbackinGCMs609

Recentprogressontheproblemofcloudfeedbackhasenabledunprecedentedadvancesinprocess-610levelunderstandingofcloudresponsestoCO2forcing.Themaincloudpropertychangesresponsible611forradiativefeedbackinGCMs–risinghighclouds,decreasingtropicallowcloudamount,increasing612lowcloudopticaldepth–aresupportedtovaryingdegreebytheoreticalreasoning,high-resolution613modeling,andobservations.614

Muchoftherecentgainsinunderstandingofradiatively-importanttropicallowcloudchangeshave615been accomplished through the use of limited-area, high-resolution LESmodels, able to explicitly616represent thecriticalboundary layerprocessesunresolvedbyGCMs.Because limited-areamodels617must be forced with prescribed climate change conditions, however, such models are unable to618representtheimportantfeedbacksofcloudsontothelarge-scaleclimate.Tofullyunderstandhow619

cloudfeedbackaffectsclimatesensitivity,atmosphericandoceaniccirculation,andregionalclimate,620wemustrelyonglobalmodels.621

Accurately representing clouds and their radiative effects in global models remains a formidable622challenge, however, andGCM spread in cloud feedback has not decreased substantially in recent623decades. Uncertainties in the global warming response of clouds are linked to the difficulty in624representing the complex interactions among the various physical processes at play – radiation,625microphysics, convective and turbulent fluxes, dynamics – through traditional GCM626parameterizations. Owing to sometimes unphysical interactions between individual627parameterizations, cloud feedback mechanisms may differ between GCMs46, 110, and these628mechanismsmayalsobedistinctfromthoseactingintherealworld.629

One approach to circumvent the shortcomings of traditional GCM parameterizations involves630embeddingacloud-resolvingmodelineachGCMgridboxoverpartofthehorizontaldomain166-168.631Such“superparameterized”GCMscanthusexplicitlysimulatesomeoftheconvectivemotionsand632subgrid variability that traditional parameterizations fail to represent accurately, while remaining633computationallyaffordablerelativetoglobalcloud-resolvingmodels.However,superparameterized634GCMsremainunabletoresolvetheboundary-layerprocessescontrollingradiatively-important low635clouds–andsimilarlytoglobalcloudresolvingmodels, theyreportdisappointingly largespread in636theircloudfeedbackestimates15.637

Arecentfurtherdevelopment,madepossiblebysteadyincreasesincomputingpower,involvesthe638useofLESratherthancloud-resolvingmodelsasasubstituteforGCMparameterizations16,169.First639results suggest encouraging improvements in the representation of boundary-layer clouds (C.640Bretherton,pers.comm.).SuperparameterizationwithLEScombinesaspectsofthemodelhierarchy641intoasinglemodel,makingitpossibletorepresentboththesmall-scaleprocessesandtheirimpact642onthelargescales.Analysesofsuperparameterizedmodelexperimentscouldalsobeusedtodesign643more realistic parameterizations to improve boundary-layer characteristics, cloud variability, and644thus cloud feedback in traditional GCMs. An important caveat, however, is that current LES645superparameterizationsarerelativelycoarseandmaynotrepresentprocessessuchasentrainment646well,sothatfurtherincreasesincomputingpowermaybenecessarytofullyexploitthepossibilities647ofLESsuperparameterization.648

Irrespectiveoffutureincreasesinspatialresolution,GCMswillcontinuerequiringparameterization649oftheimportantmicrophysicalprocessesofliquiddropletandicecrystalformation.Asdiscussedin650this review, microphysical processes constitute a major source of uncertainty in future cloud651responses, particularly with regard to mixed-phase cloud radiative properties19 and precipitation652efficiencyinconvectiveclouds107.Thetreatmentofcloud-aerosolinteractionsalsoremainsdeficient653in current parameterizations170. Improving the parameterization of microphysical processes must654therefore remain a priority for future work; this will involve a combined use of laboratory655experiments171,andsatelliteandin-situobservationsofcloudphase119,138.656

Although the main focus of this paper has been on the representation of clouds in GCMs,657observational analyses will remain crucial to advance our understanding of cloud feedback, in658conjunction with process-resolving modeling and global modeling. On the one hand, reliable659observationsof clouds and their environment at both local and global scales are indispensable to660testandimproveprocess-resolvingmodelsandGCMparameterizations.Ontheotherhand,models661

can provide process-based understanding of the relationship between clouds and the large-scale662environment,whichcanbeexploitedtoidentifyobservationalconstraintsoncloudfeedback.663

Currentlimitsofunderstanding664

We conclude this review by highlighting two problemswhichwe regard as key limitations in our665understandingofhowcloudfeedbackimpactstheclimatesystem’sresponsetoexternalforcing.The666firstproblemrelatestotherelevanceofcloudfeedbacktofutureatmosphericcirculationchanges,667which control climate change impacts at regional scales142. The circulation response is driven by668changesindiabaticheating,towhichtheradiativeeffectsofcloudsareanimportantcontribution.669Hence cloud feedbacks must affect the dynamical response to warming, but the dynamical670implicationsofcloudfeedbackarejustbeginningtobequantifiedandunderstood.Recentworkhas671shownthatcloudfeedbackshavelarge impactsontheforceddynamicalresponsetowarmingand672particularly theshiftof the jetsandstormtracks22, 161, 172, 173.Thus thecloud response towarming673appearsasoneof thekeyuncertainties for futurecirculationchanges.Substantial researchefforts674are currently underway to improve our understanding of cloud-circulation interactions at various675scalesandtheirimplicationsforclimatesensitivity,aproblemidentifiedasoneofthecurrent“grand676challenges”ofclimatescience173-175.677

Our second point concerns the problem of time dependence of cloud feedback. The traditional678feedbackanalysisframework isbasedonthesimplifyingassumptionthatfeedbackprocessesscale679with global-mean surface temperature, independent of the spatial pattern ofwarming. However,680recentresearchshowsthattheglobalfeedbackparameterdoesdependuponthepatternofsurface681warming,whichitselfchangesovertimeinCO2-forcedexperiments7,176-178.Inparticular,mostCMIP5682models subjected to an abrupt quadrupling of CO2 concentrations indicate that the SW cloud683feedbackparameterincreasesafterabouttwodecades,andthisisadirectconsequenceofchanges684intheSSTwarmingpattern179.SincefuturepatternsofSSTincreaseareuncertaininGCMs,andmay685differ fromthoseobserved inthehistoricalrecord,this introducesanadditionaluncertainty inthe686magnitudeof global-mean cloud feedback andour ability to constrain it using observations180, 181.687Therefore, further work is necessary to understand what determines the spatial patterns of SST688increase,andhowthesepatternsinfluencecloudpropertiesatregionalandglobalscales.689

690

ACKNOWLEDGMENTS691

Theauthors thank twoanonymous reviewers for their very insightful andconstructive comments.692We are also grateful to Chris Bretherton, Jonathan Gregory, Tapio Schneider, Bjorn Stevens, and693Mark Webb for helpful discussions. PC acknowledges support from the ERC Advanced Grant694“ACRCC”.DLHwassupportedbytheRegionalandGlobalClimateModelingProgramoftheOfficeof695ScienceoftheU.S.DepartmentofEnergy(DE-SC0012580).TheeffortofMDZwassupportedbythe696RegionalandGlobalClimateModelingProgramof theOfficeofScienceof theU.S.Departmentof697Energy(DOE)andbytheNASANewInvestigatorProgram(NNH14AX83I)andwasperformedunder698the auspices of the DOE by Lawrence Livermore National Laboratory under contract DE-AC52-69907NA27344. IM ReleaseLLNL-JRNL-707398. We also acknowledge the World Climate Research700Program'sWorkingGrouponCoupledModeling,which is responsible forCMIP,andwe thank the701climatemodelinggroups (listed in theSupporting Information) forproducingandmakingavailable702

theirmodeloutput.ForCMIPtheU.S.DepartmentofEnergy'sProgramforClimateModelDiagnosis703andIntercomparisonprovidescoordinatingsupportandleddevelopmentofsoftwareinfrastructure704inpartnershipwiththeGlobalOrganizationforEarthSystemSciencePortals.705

706

FURTHERREADING707

Averyusefulreviewofcloudfeedbacksinhigh-resolutionmodels:BrethertonCS.Insightsintolow-708latitude cloud feedbacks from high-resolution models. Philosophical transactions. Series A,709Mathematical,physical,andengineeringsciences2015,373:3354-3360710

Adiscussionofcloudphasechanges inhigh-latitudeclouds:StorelvmoT,Tan I,KorolevAV.Cloud711Phase Changes Induced by CO2 Warming – a Powerful yet Poorly Constrained Cloud-Climate712Feedback.CurrentClimateChangeReports2015,1:288-296713

Areviewoninteractionsbetweendynamicsandcloudsintheextratropics,includingadiscussionof714the roles of storm-track shifts in future cloud feedbacks: Ceppi P, Hartmann DL. Connections715BetweenClouds, Radiation, andMidlatitudeDynamics: a Review.Current Climate ChangeReports7162015,1:94-102717

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